Bottom Line:
As the Co composition increases, the amplitude of PMA increases first from Fe/MgO to Fe12Co4/MgO, and then decreases in Fe10Co6/MgO; finally, the magnetic anisotropy becomes horizontal in Fe8Co8/MgO.The enhanced PMA in Fe12Co4/MgO is ascribed to the optimized combination of occupied and unoccupied 3d states around the Fermi energy from both interface Fe and Co atoms, while the weaker PMA in Fe10Co6/MgO is mainly attributed to the modulation of the interface Co-d xy orbital around the Fermi energy.By adjusting the Co composition in Fe1-x Co x , the density of states of transitional metal atoms will be modulated to optimize PMA for future high-density memory application.

ABSTRACTThe perpendicular magnetic anisotropy (PMA) of Fe1-x Co x thin films on MgO(001) was investigated via first-principles density-functional calculations. Four different configurations were considered based on their ground states: Fe/MgO, Fe12Co4/MgO, Fe10Co6/MgO, and Fe8Co8/MgO. As the Co composition increases, the amplitude of PMA increases first from Fe/MgO to Fe12Co4/MgO, and then decreases in Fe10Co6/MgO; finally, the magnetic anisotropy becomes horizontal in Fe8Co8/MgO. Analysis based on the second-order perturbation of the spin-orbit interaction was carried out to illustrate the contributions from Fe and Co atoms to PMA, and the differential charge density was calculated to give an intuitive comparison of 3d orbital occupancy. The enhanced PMA in Fe12Co4/MgO is ascribed to the optimized combination of occupied and unoccupied 3d states around the Fermi energy from both interface Fe and Co atoms, while the weaker PMA in Fe10Co6/MgO is mainly attributed to the modulation of the interface Co-d xy orbital around the Fermi energy. By adjusting the Co composition in Fe1-x Co x , the density of states of transitional metal atoms will be modulated to optimize PMA for future high-density memory application.

Fig4: Majority-spin (positive) and minority-spin (negative) DOS projected to Co-3dorbital components (a-d). Fe12Co4/MgO interface (black) and Fe10Co6/MgO interface. Co1 (red) represents the Co atom at the edge of the interface, and Co2 (green) represents the Co atom in the center of the interface.

Mentions:
In the following, the contributions from Co atoms are taken into consideration. The DOS of Co-dxy, dxz,yz, , and at Fe12Co4/MgO and Fe10Co6/MgO interfaces are shown in Figure 4a,b,c,d. Since Co atoms at Fe10Co6/MgO interface are not symmetrical, we present their DOS separately. Co1 represents the Co atom at the edge of the interface, and Co2 represents the Co atom in the center of the interface. Different from Fe-dyz states, the unoccupied Co-dyz states around EF are relatively small in Fe12Co4/MgO; thus, the negative matrix element 〈x2−y2/Lx/yz〉 is much smaller than that of Fe/MgO. The other negative contribution arising from 〈yz/Lx/xy〉 is comparable to the negative matrix element 〈yz/Lx/x2−y2〉 in Fe/MgO. In addition, the positive contribution of Lz connecting occupied and unoccupied dxy states in Fe12Co4/MgO is comparable to that in Fe/MgO. In general, Co atoms in Fe12Co4/MgO contribute much more to PMA than Fe atoms in Fe/MgO. In the light of these, the PMA value contributed from both Fe and Co atoms is much larger in Fe12Co4/MgO than in Fe/MgO. In Fe10Co6/MgO, the positive matrix element 〈x2−y2/Lz/xy〉 decreases due to the reduced unoccupied dxy states for Co1 atom. It deceases even more for Co2 atom because of the very small unoccupied dxy states. Consequently, the contribution from Co atoms in Fe10Co6/MgO is much smaller than Co atoms in Fe12Co4, resulting in a relative small value of PMA.Figure 4

Fig4: Majority-spin (positive) and minority-spin (negative) DOS projected to Co-3dorbital components (a-d). Fe12Co4/MgO interface (black) and Fe10Co6/MgO interface. Co1 (red) represents the Co atom at the edge of the interface, and Co2 (green) represents the Co atom in the center of the interface.

Mentions:
In the following, the contributions from Co atoms are taken into consideration. The DOS of Co-dxy, dxz,yz, , and at Fe12Co4/MgO and Fe10Co6/MgO interfaces are shown in Figure 4a,b,c,d. Since Co atoms at Fe10Co6/MgO interface are not symmetrical, we present their DOS separately. Co1 represents the Co atom at the edge of the interface, and Co2 represents the Co atom in the center of the interface. Different from Fe-dyz states, the unoccupied Co-dyz states around EF are relatively small in Fe12Co4/MgO; thus, the negative matrix element 〈x2−y2/Lx/yz〉 is much smaller than that of Fe/MgO. The other negative contribution arising from 〈yz/Lx/xy〉 is comparable to the negative matrix element 〈yz/Lx/x2−y2〉 in Fe/MgO. In addition, the positive contribution of Lz connecting occupied and unoccupied dxy states in Fe12Co4/MgO is comparable to that in Fe/MgO. In general, Co atoms in Fe12Co4/MgO contribute much more to PMA than Fe atoms in Fe/MgO. In the light of these, the PMA value contributed from both Fe and Co atoms is much larger in Fe12Co4/MgO than in Fe/MgO. In Fe10Co6/MgO, the positive matrix element 〈x2−y2/Lz/xy〉 decreases due to the reduced unoccupied dxy states for Co1 atom. It deceases even more for Co2 atom because of the very small unoccupied dxy states. Consequently, the contribution from Co atoms in Fe10Co6/MgO is much smaller than Co atoms in Fe12Co4, resulting in a relative small value of PMA.Figure 4

Bottom Line:
As the Co composition increases, the amplitude of PMA increases first from Fe/MgO to Fe12Co4/MgO, and then decreases in Fe10Co6/MgO; finally, the magnetic anisotropy becomes horizontal in Fe8Co8/MgO.The enhanced PMA in Fe12Co4/MgO is ascribed to the optimized combination of occupied and unoccupied 3d states around the Fermi energy from both interface Fe and Co atoms, while the weaker PMA in Fe10Co6/MgO is mainly attributed to the modulation of the interface Co-d xy orbital around the Fermi energy.By adjusting the Co composition in Fe1-x Co x , the density of states of transitional metal atoms will be modulated to optimize PMA for future high-density memory application.

ABSTRACTThe perpendicular magnetic anisotropy (PMA) of Fe1-x Co x thin films on MgO(001) was investigated via first-principles density-functional calculations. Four different configurations were considered based on their ground states: Fe/MgO, Fe12Co4/MgO, Fe10Co6/MgO, and Fe8Co8/MgO. As the Co composition increases, the amplitude of PMA increases first from Fe/MgO to Fe12Co4/MgO, and then decreases in Fe10Co6/MgO; finally, the magnetic anisotropy becomes horizontal in Fe8Co8/MgO. Analysis based on the second-order perturbation of the spin-orbit interaction was carried out to illustrate the contributions from Fe and Co atoms to PMA, and the differential charge density was calculated to give an intuitive comparison of 3d orbital occupancy. The enhanced PMA in Fe12Co4/MgO is ascribed to the optimized combination of occupied and unoccupied 3d states around the Fermi energy from both interface Fe and Co atoms, while the weaker PMA in Fe10Co6/MgO is mainly attributed to the modulation of the interface Co-d xy orbital around the Fermi energy. By adjusting the Co composition in Fe1-x Co x , the density of states of transitional metal atoms will be modulated to optimize PMA for future high-density memory application.